JournalsowrVol. 6 / No. 1DOI 10.4171/owr/2009/01

Toric Geometry

  • Victor V. Batyrev

    Universität Tübingen, Germany
  • Klaus Altmann

    Freie Universität Berlin, Germany
  • Yael Karshon

    University of Toronto, Toronto, Ontario, Canada
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Abstract

Toric Geometry originated from investigations of torus actions on geometric and algebraic objects. It is addressed through algebraic geometry, symplectic geometry, equivariant topology, as well as the theory of convex polyhedra within discrete mathematics. In spite of using their own language these completely different disciplines often observe similar or even identical combinatorial phenomena. Thus toric geometry leads to a fascinating and fruitful interplay between these disciplines.